Approximate solution to the stochastic Kuramoto model
Abstract
We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators. The known critical coupling strength is exactly recovered by the Gaussian theory. Extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value. We obtain the asymptotic order parameter in closed form, which suggests a tighter upper bound for the corresponding scaling. As a last point, we elaborate the Gaussian approximation in complex networks with distributed degrees.
- Publication:
-
Physical Review E
- Pub Date:
- November 2013
- DOI:
- 10.1103/PhysRevE.88.052111
- arXiv:
- arXiv:1308.5629
- Bibcode:
- 2013PhRvE..88e2111S
- Keywords:
-
- 05.40.-a;
- 05.45.Xt;
- 87.10.Ca;
- Fluctuation phenomena random processes noise and Brownian motion;
- Synchronization;
- coupled oscillators;
- Analytical theories;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems
- E-Print:
- 6 pages, 3 figures